Google calendar events cannot be edited on my iPhone

My iPhone and my Google calendar are synced. When an event is created in Google I see it on my iPhone. I cannot however modify it in any way at all. I cannot add some new updated info, I cannot add or share this event with anyone, I cannot change the start time - I cannot edit any details ... NOTHING. For instance, I booked a trip on American Airlines. I had AA send said trip to my calendar, I see it but I cannot do anything with it. . I cannot modify the trip at all. It is completely un-editable.

Any idea how I can change this? Is it a setting in Google?

Thanks!